The invention is based on an internal combustion engine with externally supplied ignition having an ignition chamber associated with the main combustion chamber. In the German Patent Application No. P 29 16 285.4, an ignition chamber is described which is embodied in this manner. However, local overheating can occur in this embodiment at the uncooled end wall which partitions off the ignition chamber from the main combustion chamber. As a result, the occurrence of glow ignitions at the hot surface cannot be precluded.